I have learned that liquids are uncountable, except for measurements such as "three cups of water."
So, does "three lattes" in this context refer to three cups of latte?
In Australia, a few years ago, Kylie Minogue (aka 'The Singing Budgie') featured in a TV commercial for Coca Cola.
In the commercial, she ordered Two Coke, and this caused some public debate.
The answer came from the Coca Cola company itself, which I can summarise by saying Coke is a trademark and correct usage of the mark requires it to be both singular and plural — Owners of such valuable marks take these things very seriously.
But I'm not aware that anyone considers the word latte a trademark, so it should be safe to treat it as countable as jackgill described.
As a longtime restaurant worker I consider myself an expert on beverages. Coffee is brewed in quantity. We make a pot of coffee and then pour it out into cups to serve it, so the coffee is uncountable and the cups are countable. Three coffees is short for three cups of coffee, as others have noted. Latte, on the other hand, is not brewed in quantity, but individually. Each one is a separate product and can be counted. The same goes for cappuccino, espresso and their variants. You can ask for more coffee, but you ask for another latte.